# 1: What is Combinatorics?

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These notes are based on the philosophy that you learn the most about a subject when you are figuring it out directly for yourself, and learn the least when you are trying to figure out what someone else is saying about it. What we are going to try to do is to give you a chance to discover many of the interesting examples that usually appear as textbook examples and discover the principles that appear as textbook theorems.
• 1.2: Basic Counting Principles
In this section, we explore the basic counting principles through a plethora of examples and exercises. One of our goals in these notes is to show how most counting problems can be recognized as counting all or some of the elements of a set of standard mathematical objects. You may have noticed some standard mathematical words and phrases such as set, ordered pair, function, and so on creeping into the problems.
• 1.3: Some Applications of Basic Counting Principles
In this section, we explore the applications of the basic counting principles discussed in the previous section, one of which is the Pigeonhole Principle. The pigeonhole principle gets its name from the idea of a grid of little boxes that might be used, for example, to sort mail, or as mailboxes for a group of people in an office. The boxes in such grids are sometimes called pigeonholes in analogy with stacks of boxes used to house homing pigeons when homing pigeons were used to carry messages
• 1.4: What is Combinatorics? (Exercises)
This section contains the supplementary problems related to the materials discussed in Chapter 1.

Thumbnail: Logical matrices of equivalence relations. (public domain; Watchduck).